Question: Rewrite as a simplified fraction. ${0.2\overline{5} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 25.5555...\\ 10x &= 2.5555...\end{align*}}$ Subtracting the two equations, we have: ${90x = 23}$ ${x = \dfrac{23}{90}} $